(Fuzzy) hyperlattices and fuzzy preordered lattices

He, Pengfei; Xin, Xiaolong; Zhan, Jianming

doi:10.3233/ifs-130908

Cited by 6 publications

(2 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [17], Yuan and Lee gave the definition of convex fuzzy sublattices. Since fuzzy lattices and join hyperoperations have been used in engineering and computer science [18][19][20], we expect that the results of our work may be useful in similar applications. In this paper, we further discuss the convex fuzzy sublattices.…”

Section: Introductionmentioning

confidence: 86%

Some results of convex fuzzy sublattices

Xin

2014

Journal of Intelligent &Amp; Fuzzy Systems

Self Cite

View full text Add to dashboard Cite

In the present paper we give a procedure by which we generate a fuzzy ideal (resp. a fuzzy filter and a convex fuzzy sublattice) by a fuzzy set in a lattice. And we prove that a convex fuzzy sublattice generated by a fuzzy set is an intersection of a fuzzy ideal and a fuzzy filter generated by the same fuzzy set in a lattice. Moreover, the homomorphic image and pre-image of a fuzzy ideal (fuzzy filter and convex fuzzy sublattice) generated by a fuzzy set are studied. In particular, we prove that the set of convex fuzzy sublattices of a modular lattice can form a modular lattice. Finally, as an application of our main result, we give an interesting example in BCK-algebras.

show abstract

Section: Introductionmentioning

confidence: 86%

Some results of convex fuzzy sublattices

Xin

2014

Journal of Intelligent &Amp; Fuzzy Systems

Self Cite

View full text Add to dashboard Cite

show abstract

“…A. Karimi Feizabadi et al [13] studied fundamental relations in universal hyperalgebras. We have already done some work on hyper structure, for instance, in [17,18,29]. In particular, in [30,31] we introduced the concepts of states, measures, state operators and state-morphism operators on hyper BCK-algebras.…”

Section: Introductionmentioning

confidence: 99%

Hyper BL-algebras

Long¹,

Yu²,

Zhan³

2018

Filomat

View full text Add to dashboard Cite

We put forth the concept of hyper BL-algebras which is a generalization of BL-algebras. We give some non-trivial examples and properties of hyper BL-algebras. Moreover, we introduce weak filters and weak deductive systems of hyper BL-algebras and study the relationships between them. Then we state and prove some theorems about weak filters and weak deductive systems. In particular, we define the concept of regular compatible congruence on hyper BL-algebras and construct the quotient structure in hyper BL-algebras. Finally, we discuss the conditions in which a quotient hyper BL-algebra is an MV-algebra.

show abstract